Give step-by-step solution with explanation and final answer:Problem 6: (11% of Assignment Value) ¥
Aman pushes a crate up a rough slope as shown in the figure. The crate is accelerating up the slope

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Give step-by-step solution with explanation and final answer:Problem 6: (11% of Assignment Value) ¥
Aman pushes a crate up a rough slope as shown in the figure. The crate is accelerating up the slope. If
necessary, use Fs to denote the force of static friction and Fk to denote the kinetic force of friction. PY F :
Otheespertta.com
Please use the interactive area below 10 draw the Free Body Diagram for the crate.
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1Yooks ike thors i aE cast one foc tht expected the drawing, bu
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VIPSolutions · Accepted Answer

Let's break down the problem and construct the **Free Body Diagram (FBD)** for the crate being pushed up the rough slope.

---

## **Step 1: Identify All Forces Acting on the Crate**

1. **Gravity ($mg$)**: Acts vertically downward.
2. **Normal Force ($N$)**: Perpendicular to the surface of the slope, away from the surface.
3. **Applied Force ($F$)**: Up the slope, as shown by the person pushing.
4. **Friction Force ($F_k$ or $F_s$)**: Acts parallel to the surface, **opposing the motion**.  
   - Since the crate is accelerating up, **kinetic friction ($F_k$)** is acting **down the slope**.

---

## **Step 2: Draw the Free Body Diagram**

### **Coordinate Axes**
- $x$-axis: Along the incline (up the slope is positive)
- $y$-axis: Perpendicular to the incline (outward from the surface)

### **Forces:**
- **Gravity ($mg$)**: Drawn straight downward from the crate's center.
- **Normal Force ($N$)**: Perpendicular to the slope, away from the surface.
- **Applied Force ($F$)**: Parallel to the slope, up the incline.
- **Kinetic Friction ($F_k$)**: Parallel to the slope, **down** the incline.

---

## **Step 3: Explanation of Each Force Direction**

- **Gravity ($mg$)**: Always straight down.
- **Normal ($N$)**: Always perpendicular outward from the contact surface.
- **Applied ($F$)**: Shown pushing the crate up the ramp.
- **Friction ($F_k$)**: Opposes motion, so if crate is moving up, friction acts down the ramp.

---

## **Step 4: Visual Representation**

Here's a diagram for reference:

```
         /|
        /_|_________  θ = angle of incline
       /  |       ↑
      /   |      N (normal)
     /    |
    /_____|
   |      / 
   |     / 
   |    / crate
       ●  ← (F) applied force (up slope)
       ↑
       |
      (F_k) kinetic friction (down slope)

Gravity (mg) acts vertically down from the crate's center
```

---

### **Summary Table of Forces**

| Force            | Direction                           | Label        |
|------------------|-------------------------------------|--------------|
| Gravity          | Downward (vertical)                 | $mg$       |
| Normal           | Perpendicular to surface (outward)  | $N$        |
| Applied          | Up the slope                        | $F$        |
| Kinetic Friction | Down the slope                      | $F_k$      |

---

## **Final Answer:**

### **The FBD for the crate should include:**

- **Gravity ($mg$)**: Downward.
- **Normal force ($N$)**: Perpendicular and away from the surface.
- **Applied force ($F$)**: Up the ramp (same direction as motion).
- **Kinetic friction ($F_k$)**: Down the ramp (opposite to motion).

---

**Tip:**  
When drawing in the interactive area, make sure arrows start from the crate's center and point in the correct directions as explained above.

---

**Let me know if you need a sketched version, or help with the equations of motion!**

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